**9/05/2014****
**Given
y = 2/(e^{x}
+ e^{-}^{x}),
solve for *x
*in
terms of *y*.

**Scroll
down for the solution.**

**9/05/2014
**Solution.
**Since
****y
= 2/(e**^{x}**
+ e**^{-}^{x}**),
cross-multiplying, we get:**

**ye**^{x}**
+ ye**^{-}^{x}*
***=
2**

**Rewriting:
ye**^{x}**
+ y****·****
1/****e**^{x}**
= 2Multiplying by the LCD of e**

Rewriting and rearranging: y(e

Using the quadratic formula: e

Factoring out the 4 from inside the

e

so that switching to